The Effect of Shill Bidding upon Prices: Experimental Evidence

This paper explores, through a series of experiments, the effect of shill bidding upon revenues and prices in auctions. We study the practice of shill bidding in a common value framework. Our findings are consistent with the theoretical prediction that, if bidders are aware of the possibility of seller participation in an auction, shill bidding lowers profits on average. Shill bidding can alleviate the problem of the winner's curse by lowering the price and it can, thus, provide benefits to the bidders. Finally, even though there were too many bidders that submitted bids in these auctions, the number of entrants was not affected by the possibility of seller participation, which is also consistent with the theory.Auctions, Experiment, Shill Bidding, Entry

Optimal takeover contests with toeholds

This paper characterizes how a target firm should be sold when the possible buyers (bidders) have prior stakes in its ownership (toeholds). We find that the optimal mechanism needs to be implemented by a non-standard auction which imposes a bias against bidders with high toeholds. This discriminatory procedure is such that the target´s average sale price is increasing in both the size of the common toehold and the degree of asymmetry in these stakes. It is also shown that a simple mechanism of sequential negotiation replicates the main properties of the optimal procedure and yields a higher average selling price than the standard auctions commonly used in takeover battles

Order Flow and the Formation of Dealer Bids: An Analysis of Information and Strategic Behavior in the Government of Canada Securities Auctions

Using data on Government of Canada securities auctions, this paper shows that in countries where direct access to primary issuance is restricted to government securities dealers, Order-flow" information is a key source of private information for these security dealers. Order-flow information is revealed to a security dealer through his interactions with customers, who can place bids in the auctions only through the security dealer. Since each dealer interacts with a different set of customers, they, in effect, see different portions of the market demand and supply curves, leading to differing private inferences of where the equilibrium price might.Treasury auctions, Behavioural finance

Decentralized Learning for Multi-player Multi-armed Bandits

We consider the problem of distributed online learning with multiple players in multi-armed bandits (MAB) models. Each player can pick among multiple arms. When a player picks an arm, it gets a reward. We consider both i.i.d. reward model and Markovian reward model. In the i.i.d. model each arm is modelled as an i.i.d. process with an unknown distribution with an unknown mean. In the Markovian model, each arm is modelled as a finite, irreducible, aperiodic and reversible Markov chain with an unknown probability transition matrix and stationary distribution. The arms give different rewards to different players. If two players pick the same arm, there is a "collision", and neither of them get any reward. There is no dedicated control channel for coordination or communication among the players. Any other communication between the users is costly and will add to the regret. We propose an online index-based distributed learning policy called ${\tt dUCB_4}$ algorithm that trades off \textit{exploration v. exploitation} in the right way, and achieves expected regret that grows at most as near-$O(\log^2 T)$. The motivation comes from opportunistic spectrum access by multiple secondary users in cognitive radio networks wherein they must pick among various wireless channels that look different to different users. This is the first distributed learning algorithm for multi-player MABs to the best of our knowledge.Comment: 33 pages, 3 figures. Submitted to IEEE Transactions on Information Theor

Optimal takeover contests with toeholds

This paper characterizes how a target firm should be sold when the possible buyers (bidders) have prior stakes in its ownership (toeholds). We find that the optimal mechanism needs to be implemented by a non-standard auction which imposes a bias against bidders with high toeholds. This discriminatory procedure is such that the target´s average sale price is increasing in both the size of the common toehold and the degree of asymmetry in these stakes. It is also shown that a simple mechanism of sequential negotiation replicates the main properties of the optimal procedure and yields a higher average selling price than the standard auctions commonly used in takeover battles.Optimal auctions, Takeovers, Toeholds, Asymmetric auctions

Stochastic control in limit order markets

In dieser Dissertation lösen wir eine Klasse stochastischer Kontrollprobleme und konstruieren optimale Handelsstrategien in illiquiden Märkten. In Kapitel 1 betrachten wir einen Investor, der sein Portfolio nahe an einer stochastischen Zielfunktion halten möchte. Gesucht ist eine Strategie (aus aktiven und passiven Orders), die die Abweichung vom Zielportfolio und die Handelskosten minimiert. Wir zeigen Existenz und Eindeutigkeit einer optimalen Strategie. Wir beweisen eine Version des stochastischen Maximumprinzips und leiten damit ein Kriterium für Optimalität mittels einer gekoppelten FBSDE her. Wir beweisen eine zweite Charakterisierung mittels Kauf- und Verkaufregionen. Das Portfolioliquidierungsproblem wird explizit gelöst. In Kapitel 2 verallgemeinern wir die Klasse der zulässigen Strategien auf singuläre Marktorders. Wie zuvor zeigen wir Existenz und Eindeutigkeit einer optimalen Strategie. Im zweiten Schritt beweisen wir eine Version des Maximumprinzips im singulären Fall, die eine notwendige und hinreichende Optimalitätsbedingung liefert. Daraus leiten wir eine weitere Charakterisierung mittels Kauf-, Verkaufs- und Nichthandelsregionen ab. Wir zeigen, dass Marktorders nur benutzt werden, wenn der Spread klein genug ist. Wir schließen dieses Kapitel mit einer Fallstudie über Portfolioliquidierung ab. Das dritte Kapitel thematisiert Marktmanipulation in illiquiden Märkten. Wenn Transaktionen einen Einfluß auf den Aktienpreis haben, dann können Optionsbesitzer damit den Wert ihres Portfolios beeinflussen. Wir betrachten mehrere Agenten, die europäische Derivate halten und den Preis des zugrundeliegenden Wertpapiers beeinflussen. Wir beschränken uns auf risikoneutrale und CARA-Investoren und zeigen die Existenz eines eindeutigen Gleichgewichts, das wir mittels eines gekoppelten Systems nichtlinearer PDEs charakterisieren. Abschließend geben wir Bedingungen an, wie diese Art von Marktmanipulation verhindert werden kann.In this thesis we study a class of stochastic control problems and analyse optimal trading strategies in limit order markets. The first chapter addresses the problem of curve following. We consider an investor who wants to keep his stock holdings close to a stochastic target function. We construct the optimal strategy (comprising market and passive orders) which balances the penalty for deviating and the cost of trading. We first prove existence and uniqueness of an optimal control. The optimal trading strategy is then characterised in terms of the solution to a coupled FBSDE involving jumps via a stochastic maximum principle. We give a second characterisation in terms of buy and sell regions. The application of portfolio liquidation is studied in detail. In the second chapter, we extend our results to singular market orders using techniques of singular stochastic control. We first show existence and uniqueness of an optimal control. We then derive a version of the stochastic maximum principle which yields a characterisation of the optimal trading strategy in terms of a nonstandard coupled FBSDE. We show that the optimal control can be characterised via buy, sell and no-trade regions. We describe precisely when it is optimal to cross the bid ask spread. We also show that the controlled system can be described in terms of a reflected BSDE. As an application, we solve the portfolio liquidation problem with passive orders. When markets are illiquid, option holders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. In Chapter 3, we consider a model with competing players that hold European options and whose trading has an impact on the price of the underlying. We establish existence and uniqueness of equilibrium results and show that the equilibrium dynamics can be characterised in terms of a coupled system of non-linear PDEs. Finally, we show how market manipulation can be reduced

Bidding in common value fair division games: The winner's curse or even worse?

A unique indivisible commodity with an unknown common value is owned by group of individuals and should be allocated to one of them while compensating the others monetarily. We study the so-called fair division game (Güth, Ivanova-Stenzel, Königstein, and Strobel (2002, 2005)) theoretically and experimentally for the common value case and compare our results to the corresponding common value auction. Whereas symmetric risk neutral Nash equilibria are rather similar for both games, behavior differs strikingly. Implementing auctions and fair division games in the lab in a repeated setting under first- and second-price rule, we find that overall behavior is much more dispersed for the fair division games than for the auctions. Winners' profit margins and shading rates are on average slightly lower for the fair division game. Moreover, we find that behavior in the fair division game separates into extreme over- and underbidding.common value auction, winner's curse, fair division game

Liquidity Effects of Trading Frequency

In this article, we present a discrete time modeling framework, in which the shape and dynamics of a Limit Order Book (LOB) arise endogenously from an equilibrium between multiple market participants (agents). We use the proposed modeling framework to analyze the effects of trading frequency on market liquidity in a very general setting. In particular, we demonstrate the dual effect of high trading frequency. On the one hand, the higher frequency increases market efficiency, if the agents choose to provide liquidity in equilibrium. On the other hand, it also makes markets more fragile, in the sense that the agents choose to provide liquidity in equilibrium only if they are market-neutral (i.e., their beliefs satisfy certain martingale property). Even a very small deviation from market-neutrality may cause the agents to stop providing liquidity, if the trading frequency is sufficiently high, which represents an endogenous liquidity crisis (aka flash crash) in the market. This framework enables us to provide more insight into how such a liquidity crisis unfolds, connecting it to the so-called adverse selection effect.Comment: Accepted in Mathematical Financ

Relying on the Information of Others: Debt Rescheduling with Multiple Lenders

Can inertia in terminating unsuccessful loans (creditor passivity) be due to the multiplicity of lenders in loan arrangements? Can a lender reschedule, betting against his odds? Private information in the form of bad but coarse news, that would prompt foreclosure on its own, will instead lead to rescheduling. The gamble is that other lenders may have sharper information. At equilibrium, rescheduling occurs even if all lenders received bad news. This is ine¢ cient (increasing the cost of capital) compared to perfect information sharing. However, barren information sharing, at equilibrium there is no excess reliance on the information of others from a social point of view. The paper also contains an extension dealing with \"�financial scandals\".Debt contracts, asymmetric information, rescheduling, in- solvency, Bayesian games.

Relying on the Information of Others: Debt Rescheduling with Multiple Lenders

Can inertia in terminating unsuccessful loans be due to the multiplicity of lenders in loan arrangements? Can a lender reschedule, betting against his odds? We show that fear of being last in a liquidation run prevents the aggregation of the lenders' information about the value of continuation. Private information in the form of bad but coarse news, that would prompt foreclosure on its own, will instead lead to rescheduling. The gamble is that other lenders may have sharper information. At equilibrium, rescheduling occurs even if all lenders received bad news. This is inefficient (increasing the cost of capital) compared to perfect information sharing. However, from a social point of view, barren information sharing, the equilibrium does not exhibit excessive reliance on the information of others.Debt contracts, asymmetric information, rescheduling, bankruptcy, Bayesian games